Such a fuel injection device is known from the brochure "Reliable Electronic Injection with Future Fuel Qualities" of the MAN company, dated April 1980. The fuel injection device described in the beforementioned brochure is designed for use with a two-stroke marine diesel engine. This fuel injection device has a fuel pressure reservoir, from which the fuel, at an approximately constant pressure of approximately 700 bar, can be withdrawn under electronic control for delivery to the individual injection valves. This entire control is constructed so that, in addition to the electronic control, it further requires a working fluid in the form of a hydraulic fluid, with which the individual valves and control elements are actuated. Further, the components "cylinder unit and high-pressure pump," which are illustrated at least approximately to scale, are arranged far apart so that, together with the fuel pressure reservoir arranged at another location on the internal combustion engine, long connecting lines are needed for the pressurized fuel. Because of the long lines, the system as a whole is hydraulically soft, so that the advantages achievable in principle with the illustrated fuel injection system are not achieved.